Qualifications
Size, speed, strength, size, experience as a football player at the highest schoolboy levels, size, strength, additional experience in other sports, size, speed, a can-do attitude, size, size, size, and size.
Strictly speaking, one doesn't have to play college football to become an NFL player. NFL rules say that a player entering the draft must be at least three years removed from his final year of high school, but make no mention of college (source). For example, a player with no college football experience named Carlton Haselrig was chosen in the twelfth round of the 1989 draft. Haselrig played for five seasons, and made one Pro Bowl.
The catch is, he was also one of the best collegiate wrestlers ever—he is the only person ever to win six NCAA championships in three years. So while it's possible to become an excellent professional football player without college experience, you still need to be a world-class athlete, preferably with at least one victory over 1996 Olympic gold medalist Kurt Angle.